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Transcript
```Outline
• Selection on:
– Overdominant traits
– Underdominant traits
How much selection is enough?
• In the idealized situations we are examining:
– ANY selection will cause an increase of the favored allele
– Speed of response will depend on strength of selection and dominance
structure
• In real situations:
– Effective selection must be strong enough to overcome drift (random
effects)
– Effective selection must be strong enough to have an impact in
reasonable time scale
• Selection will dominate evolution if it’s stronger than drift
• This depends critically on population size
Overdominance = heterozygote most fit
• Sickle-cell trait (in presence of malaria)
• Large size of many cultivated crop plants
Overdominance
Surprising things happen when the heterozygote is most fit.
This example uses pA = pa = 0.5.
Genotype
Fitness
Before selection
Death due to selection
After selection
After selection
New allele frequencies:
pA = 0.5
pa = 0.5
black/black (AA)
0.8
0.25
0.05
0.2/0.9
0.22
black/red (Aa)
1.0
0.5
0.0
0.5/0.9
0.56
red/red (aa)
0.8
0.25
0.05
0.2/0.9
0.22
Overdominance
• Strong selection is acting, but the allele frequencies did not change. The
population is at an equilibrium state.
• If the initial frequencies were not 50/50, the population would move
towards 50/50 and then stick there.
• The ratio 50/50 is because the homozygotes are equally bad. If they
were unequally bad, a different ratio would be obtained.
Overdominance Practice Problem
The classic sickle cell case may have selection approximately like this (in
the presence of malaria):
Genotype
Fitness
AA
0.8
AS
1.0
SS
0.0
If we start with pA=0.6, what are the genotype frequencies in adults (after
selection) next generation? What are the new allele frequencies?
Overdominance
The classic sickle cell case may have selection approximately like this (in
the presence of malaria). Starting with pA=0.6:
Genotype
Fitness
Before selection
Death due to selection
After selection
After selection
AA
0.8
0.36
0.07
0.29/0.77
0.38
AS
1.0
0.48
0.0
0.48/0.77
0.62
pA=0.69, so it’s increasing.
How can we predict the stable equilibrium?
SS
0.0
0.16
0.16
0.0/0.77
0.00
Overdominance
If we write the fitnesses like this:
Genotype
Fitness
AA
1-s
AS
1.0
SS
1-t
then the equilibrium frequency of A is this:
t/(s+t)
So in our example where s=0.2 and t=1.0, pA at equilibrium is:
1.0 / (0.2 + 1.0) = 0.8333
Overdominance
• Overdominant systems have a stable equilibrium:
– If undisturbed, they will stay there
– If moved away, they will return
• Population maximizes its overall fitness given the laws of Mendelian
segregation.
• An all-heterozygote population would be more fit, but is prevented by
random mating and segregation
• A population with HbA and HbS pays two costs:
– A/A people die of malaria
– S/S people die of sickle cell anemia
Overdominance
Hard versus soft selection
• Soft selection:
– Overall population size does not change
– Requires excess reproductive capacity
• Hard selection:
– Population size decreases until bad genotypes are gone
– Selection is strong enough to overcome excess reproduction
• (Our calculations so far assume soft selection)
• Every overdominant locus has a cost (bad homozygotes)
• How many can a species stand?
• Depends on:
– How bad the homozygotes are
– How much excess reproductive capacity the species has
• Relatively few overdominant loci have been detected in wild populations
Overdominance versus drift effects–discussion question
• We cross purebred domestic plants or animals
• The crosses are larger, healthier, or more productive than their parents
• Two hypotheses:
– Overdominance
– Each purebred has bad recessives which are masked in the hybrid
• How could we decide between these hypotheses?
Overdominance versus drift effects
• Repeatedly backcross to one of the parent strains, selecting for the best
offspring
• If the hybrid vigor is due to overdominance it will never “breed true”
• If the hybrid vigor is due to good dominants covering up bad recessives,
we can improve our parent strain by crossing them in
• Eventually we will get a purebred strain that is better than before
Underdominance = heterozygote least fit
• Diabetes risk is worst in HLA-DR 3/4
heterozygote
• Mimic butterflies (see next slide)
Underdominance
In the African butterfly Pseudacraea eurytus the orange and blue
homozygotes each resemble a local toxic species, but the heterozygote
resembles nothing in particular and is attractive to predators.
Underdominance
What happens to an underdominant locus, like the mimic butterflies?
pA = pa = 0.5
Genotype
Fitness
Before selection
Selection deaths
After selection
After selection
orange/orange (AA)
1.0
0.25
0
0.25/0.9
0.28
New allele frequencies:
pA = 0.5
pa = 0.5
orange/blue (Aa)
0.8
0.5
0.1
0.4/0.9
0.44
blue/blue (aa)
1.0
0.25
0
0.25/0.9
0.28
Underdominance
The heterozygote is bad, but with equal badness and equal frequencies,
the population balances at an equilibrium. However, this equilibrium is
unstable. If the gene frequencies are not at the equilibrium, they will move
away until either A or a is fixed.
Underdominance
Again, we can predict the equilibrium by writing the fitnesses as follows:
Genotype
Fitness
orange/orange (AA)
1-s
orange/blue (Aa)
1
blue/blue (aa)
1-t
but now both s and t are negative. The unstable equilibrium is
pA = t/(s+t)
If pA is above the equilibrium, A will fix. If pA is below the equilibrium, a
will fix. If it is exactly at the equilibrium, chance will eventually push it one
way or the other.
Underdominant loci are usually observed only in crosses between separate
varieties or species. Within one population, they are rapidly fixed for one
allele or the other.
Underdominance
Underdominance practice problem
Genotype
Fitness
Fitness
black/black (AA)
1-s
1.5
black/red (Aa)
1
1.0
What is the equilibrium?
If we start at pA=0.2, what will happen?
red/red (aa)
1-t
1.2
Underdominance
Genotype
Fitness
Fitness
black/black (AA)
1-s
1.5
black/red (Aa)
1
1.0
red/red (aa)
1-t
1.2
The equilibrium is pA=0.28. So if the starting position is below this, the
a allele will win and become fixed even though this does not maximize
population fitness. The population rolls to a small fitness peak, even
though a larger one is possible.
Underdominance
• Population which is fixed for a resists introduction of A
• Innovations which are bad in heterozygotes are hard to establish
• How can they ever get established?
–
–
–
–
Genetic drift in a small population
Founder effect
Bottleneck
Inbreeding or self-fertilization (makes homozygotes)
Big changes in genome structure are underdominant
An underdominance mystery
• Insulin-dependent (juvenile) diabetes is a life-threatening disease
• Prior to insulin treatment most affected individuals died before they could
reproduce
• High-risk HLA genotype is DR3/DR4 heterozygote
• In Europeans, p(DR3) around 0.12 and p(DR4) around 0.15
• In a system with only DR3 and DR4, what would you expect in the long
term?
An underdominance mystery
• DR3 and DR4 are both old alleles
• The problems in the heterozygote could drive one of them extinct
• (We don’t know which one without knowing fitness of homozygotes)
• This hasn’t happened: why?
An underdominance mystery
Some possibilities:
• DR3/DR4 could be a generally good genotype despite diabetes risk
• Diabetes risk could reflect a linked gene that hasn’t been there long
• Presence of many other alleles may interfere with selection on 3 and 4
• Modern environment may be different from the past
• Genetic drift
Human fitnesses are hard to measure, so this question is still unsolved
• Traits on the Y are easy to analyze
• They are haploid, so dominance and recessiveness don’t matter
• Traits on the X behave more strangely
Suppose that among X chromosomes, p(X H ) = 0.8 and p(X h) = 0.2 in
both sexes.
Genotype
Fitness
Pre-Selection Frequencies
XHXH
1.0
0.32
XHXh
1.0
0.16
X hX h
0.1
0.02
XHY
1.0
0.40
X hY
0.1
0.10
We can see immediately that a rare recessive sex-linked disease shows up
mostly in males.
Genotype
Fitness
Pre-Selection Frequencies
Post-Selection Frequencies
XHXH
1.0
0.32
0.36
XHXh
1.0
0.16
0.19
X hX h
0.0
0.02
0.0
XHY
1.0
0.40
0.45
X hY
0.0
0.10
0.0
The new allele frequencies are:
Females: p(X H ) = 0.91, p(X h) = 0.09
Males: p(X H ) = 1.0, p(X h) = 0.0
This is an example of a situation where Hardy-Weinberg will not hold next
generation, because you don’t have random mating. Males must mate with
females, and their allele frequencies differ.
• This trait will decrease faster than an autosomal recessive because it is
exposed to selection when in males
• Sex-linked traits don’t go to Hardy-Weinberg in one generation like
autosomal traits do, even if there is no selection.
• Without selection, they go to Hardy-Weinberg slowly over many
generations
• With selection, they may never get there
• A point to bear in mind:
– Most sex-specific traits are not sex-linked
– They are sex-modified or sex-limited (their phenotype is controlled by
sex) but the genes are actually on the autosomes
– Most sex-linked traits (on the sex chromosomes) are unrelated to sex
– Examples: hemophilia, color vision
– The Y chromosome contains a few “switch” genes which control sex
in humans
– Almost all of the genes controlled by these switches are autosomal
• Why?
The only Y-linked non-sex gene I know of
• Why aren’t sex-related traits sex-linked?
• Putting female traits on the X would run into the problem that males
have an X too
• Why aren’t male traits on the Y?
– If sex-related traits evolved from other traits, they would tend to start
off on the autosomes
– The Y is haploid and mostly non-recombining, which can cause its
genes to deteriorate
– Having one master switch rather than many independent sex-related
trait genes may be less fragile
One-minute responses
• Tear off a half-sheet of paper
• Write one line about the lecture:
– Was anything unclear?
– Did anything work particularly well?
– What could be better?
• Leave at the back on your way out
```
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